Detecting dark matter substructure spectroscopically in strong gravitational lenses

The Cold Dark Matter (CDM) model for galaxy formation predicts that a significant fraction of mass in the dark matter haloes that surround L L* galaxies is bound in substructures of mass 1E4-1E7Msun. The number of observable baryonic substructures (such as dwarf galaxies and globular clusters) falls short of these predictions by at least an order of magnitude. We present a method for searching for substructure in the haloes of gravitational lenses that produce multiple images of QSOs, such as 4-image Einstein Cross lenses. Current methods based on broadband flux ratios cannot cleanly distinguish between substructure, differential extinction, microlensing and, most importantly, ambiguities in the host lens model. These difficulties may be overcome by utilizing the prediction that when substructure is present, the magnification will be a function of source size. QSO broad line and narrow line emission regions are approximately ~1pc and >100pc in size, respectively. When narrow line region (NLR) features are used as a normalisation, the relative intensity and equivalent width of broad line region (BLR) features will respectively reflect substructure-lensing and microlensing effects. Spectroscopic observations of just a few image pairs would probably be able to cleanly extract the desired substructure signature and distinguish it from microlensing. In the rest-optical, the Hbeta/[OIII] region is ideal, since the narrow wavelength range also largely eliminates differential reddening problems. Simulations of Q2237+030 are done as an example to determine the level of substructure that is detectable in this way, and possible systematic difficulties are discussed. This is an ideal experiment to be carried out with near-infrared integral field unit spectrographs on 8-m class telescopes.